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This survey highlights the recent advances in algorithms for numerical linear algebra that have come from the technique of linear sketching, whereby given an n X d matrix A, one first compresses A to an m X d matrix S - A, where S is a certain m X n random matrix with m " n. Much of the expensive computation is then performed on S - A, thereby accelerating the solution for the original problem involving A. This book considers least squares as well as robust regression problems, low rank approximation, and spectral sparsification. It also discusses a number of variants of these problems. Finally, it discusses the limitations of this method.